Quantum oscillators prepared out of thermal equilibrium can be used to produce work and transmit information. By intensive cooling of a single oscillator, its thermal energy deterministically dissipates to a colder environment, and the oscillator substantially reduces its entropy. This out-of-equilibrium state allows us to obtain work and to carry information. Here, we propose and experimentally demonstrate an advanced approach, conditionally preparing more efficient out-of-equilibrium states only by a weak dissipation, an inefficient quantum measurement of the dissipated thermal energy, and subsequent triggering of that states. Although it conditionally subtracts the energy quanta from the oscillator, average energy grows, and second-order correlation function approaches unity as by coherent external driving. On the other hand, the Fano factor remains constant and the entropy of the subtracted state increases, which raise doubts about a possible application of this approach. To resolve it, we predict and experimentally verify that both available work and transmitted information can be conditionally higher in this case than by arbitrary cooling or adequate thermal heating up to the same average energy. It qualifies the conditional procedure as a useful source for experiments in quantum information and thermodynamics.
Quantum oscillators prepared out of thermal equilibrium can be used to produce work and transmit information. By intensive cooling of a single oscillator, its thermal energy deterministically dissipates to a colder environment, and the oscillator substantially reduces its entropy. This out-of-equilibrium state allows us to obtain work and to carry information. Here, we propose and experimentally demonstrate an advanced approach, conditionally preparing more efficient out-of-equilibrium states only by a weak dissipation, an inefficient quantum measurement of the dissipated thermal energy, and subsequent triggering of that states. Although it conditionally subtracts the energy quanta from the oscillator, average energy grows, and second-order correlation function approaches unity as by coherent external driving. On the other hand, the Fano factor remains constant and the entropy of the subtracted state increases, which raise doubts about a possible application of this approach. To resolve it, we predict and experimentally verify that both available work and transmitted information can be conditionally higher in this case than by arbitrary cooling or adequate thermal heating up to the same average energy. It qualifies the conditional procedure as a useful source for experiments in quantum information and thermodynamics.
Thermodynamics is a phenomenological theory describing the energy conversion of work and heat. At its origins thermodynamics was developed in order to understand and improve heat engines. In conventional thermodynamics, however, only such processes are completely describable which are slow enough to keep the system of interest in an equilibrium state with its thermal environment at all times. On the contrary, all real physical processes are accompanied by non-equilibrium phenomena. These are mathematically described with the help of the irreversible entropy production, i.e. the dissipated work divided by the temperature of the bath. The second law of thermodynamics merely states that the irreversible entropy production is on average always positive. The modern trend of miniaturization, however, leads to smaller and smaller devices. On short length scales thermal noise as well as quantum fluctuations become important. Thus, usual thermodynamic quantities as work and heat acquire stochastic nature. Moreover, in the quantum regime a completely new theory had to be invented, since classical notions of work and heat are no longer valid. The present dissertation contributes to this prevailing field by the derivation of analytical expressions for the entropy production in open and closed quantum system far from thermal equilibrium. The theoretical treatment is motivated by an experimental point of view. The obtained results were derived from the reduced dynamics of the quantum mechanical system, which may be coupled to a thermal bath. To this end, it was dealt with methods and approaches of statistical physics, conventional thermodynamics, quantum information theory and the theory of open quantum systems. In this dissertation the most important physical systems are treated. First, an isolated system is considered before later on a heat bath is included. The limit of weak as well as of strong coupling are analyzed in detail. For isolated systems it turns out that a geometric approach is able to capture the thermodynamic properties, completely. To this end, the irreversible entropy production is sharply estimated from below by the angle between the real non-equilibrium state and the corresponding equilibrium one. Further, it is shown that the Heisenberg uncertainty relation for energy and time can be formulated more precisely in terms of that angle. As experimental system cold ion traps are introduced, in which the theoretical predictions can be verified. For weakly coupled systems, then, the irreversible entropy production is identified and a fluctuation theorem is derived by merely thermodynamic arguments. As experimental system we, again, propose the cold ion traps, where the heat bath can be simulated with the help of LASER light. In the limit of strong coupling a semiclassical description of the reduced quantum system is discussed. Again, an analytically exact expression for the entropy production and the corresponding fluctuation theorem is derived. A physical system, in which strong coupling to the environment can be analyzed, is given by Josephson junctions. This dissertation discusses the entropy production for isolated, weakly coupled, and overdamped quantum systems. For these physical regimes analytical relation are derived and experimental systems proposed, with which the predictions can be verified.
We use a canonical quantization procedure to set up a quantum Fokker-Planck-Kramers equation that accounts for quantum dissipation in a thermal environment. The dissipation term is chosen to ensure that the thermodynamic equilibrium is described by the Gibbs state. An expression for the quantum entropy production that properly describes quantum systems in a nonequilibrium stationary state is also provided. The time-dependent solution is given for a quantum harmonic oscillator in contact with a heat bath. We also obtain the stationary solution for a system of two coupled harmonic oscillators in contact with reservoirs at distinct temperatures, from which we obtain the entropy production and the quantum thermal conductance.
We develop an exact analytical framework for studying the nonequilibrium dynamics of interacting quantum harmonic oscillators coupled to a modelled thermal reservoir and driven by external classical fields. The total Hamiltonian is diagonalized via successive Bogoliubov transformations, enabling a nonperturbative treatment of dissipation and driving. For two coupled oscillators with an external source applied to the first, we derive explicit energy expressions and analyze their dependence on coupling and bath parameters. The phase-space structure is characterized through Husimi Q-functions for initial separable coherent and number states. We obtain the reduced density matrix elements in the number-state basis and demonstrate that, in the absence of driving and at zero temperature, the reduced density matrix of the main system satisfies the Lindblad master equation. A generating function for the Husimi function is introduced to facilitate computation of higher-order correlations. The analysis is then generalized to n interacting oscillators, with analytical energy expressions provided and the case n=3 examined in detail. Our results establish a versatile and exact framework for driven-dissipative quantum systems, with potential applications in quantum thermodynamics, open quantum systems, and many-body physics.
Quantum thermodynamics (QT) is an emerging field of research that aims to investigate how the laws of thermodynamics and quantum mechanics merge together in small quantum systems.With advances at the necessary technology to control and measure those small physical systems this field has acquired even more importance, not only in the sense that it can be tested, which is a good thing for basic research, but that new applications could be implemented at these scales, so a better comprehension of the limitations imposed by quantum thermodynamics turns out to be of crucial importance for these goals, which forces theoreticians to produce experimentally relevant versions of these new concepts.Another important aspect present at those systems is that part of them work in a regime where its constituents are described by non-thermal states, and in particular non-thermal steady states, which brings to light a different thermodynamic description, usually called steady-state thermodynamics, therefore one of the goals that we are willing to achieve with this thesis is to give an introduction to QT of systems out-of-equilibrium.One of the related subtopics that physicists deal with in QT and the one that we will be focusing on this work are the use of non-thermal stationary states to build heat engines in the quantum domain, and the analyses of the features that this new regime could possibly allow, like the use of quantum resources as a way to overcome classical limitations imposed on its performance, like to attain efficiencies higher than Carnot's or operate in certain regimes unattainable using only classical resources.Therefore, in order to clarify the underlying physics of those systems in a non-thermal regime, any experimentally well suited content is more than welcome.So keeping that in mind we devised an experimentally relevant thermodynamic cycle for a transmon qubit WS interacting with a non-thermal environment composed by two subsystems, an externally excited cavity and a classical heat bath with temperature T. The WS undergoes a non-conventional cycle (different from Otto, Carnot, etc.) through a succession of non-thermal stationary states obtained by slowly varying its bare frequency and the amplitude of the field applied on the cavity.The efficiency of this engine obtains a maximum value up to 47% in the regime of operation used.We also wanted to look for the role played by the different types of coherences, present at the WS, on the behavior of the engine and its efficiency.By different types of coherence we mean the so called modes of coherence, whose definition is based on how they respond to symmetry transformations.We did that for the trivial case of the qubit, that only contains the modes 1 and -1, and that has shown to be extremely important for the efficiency of the machine.The same procedure was repeated for a 3-level system WS.The modes 1 and -1 was again very important, not only to the absolute value of the engine's efficiency but to the regime of operation of the machine.The additional modes, 2 and -2, had a negative impact on the efficiency, reducing its absolute value.This result appears to show some evidences that quantumness won't necessarily bring improvements to the operation of those machines.
Recent theoretical and experimental work on the foundations of statistical mechanics and thermodynamics has shown that quantum pure states typically evolve to thermal equilibrium. We focus on formulating the second law of thermodynamics for these states. The standard quantum von Neumann quantum entropy is constant during equilibration, S^{vN}=0, in apparent conflict with the entropy increase of the second law, ΔS_{univ} > 0. We explore a recently developed entropy S_{univ}^Q for a pure state and test its behavior in simulations of a model system and environment evolving in time with heat flow to equilibrium. We find that the entropy approaches the correct classical value in a type of classical limit with weak coupling. With stronger coupling, we find a new source of quantum "excess entropy production," which has its origin in the quantum spreading of the wavepacket. Are there quantum thermodynamic effects related to this new source of entropy? To test this, we developed a model for a small variable temperature quantum oscillator bath. We performed simulations where two small baths are linked by a system, with unequal couplings to the baths. The model evolves to a novel type of equilibrium state with unequal temperatures in the baths, with heat flow from cold to hot along the path to equilibrium. We give an account of this behavior in terms of the second law with the quantum entropy S_{univ}^Q. The new formulation of the second law thus appears well-founded and fruitful, with surprising new quantum thermodynamic effects that may still be awaiting discovery, for example in molecules or systems far from equilibrium. \n\nThis dissertation includes previously published and unpublished co-authored material.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.